Which is larger, the sum of the first 22 even natural numbers or the sum of the first 22 odd natural numbers, and by how much?

Evens: 2, 4, ..., 44, so $S=\frac{22}{2}$$(2+44)=11(46)=506$. Odds: 1, 3, ..., 43, so $S=22^2=484$. The evens win by 506 - 484 = 22. This is no accident: each even number is exactly 1 more than the odd number in the same position, so over 22 positions the gap is 22, not 44. The two sums are never equal for any $n>0$.